How many grams of copper will be replaced in 2L of a 1.50 M `CuSO_(4)` solution if the latter is made to react with 27.0 of aluminium (Cu=63.5, AI= 27.0)

Options

A. `190.50g`
B. `95.25g`
C. `31.75g`
D. `10.65g`

Explanation

To solve the problem of how many grams of copper will be replaced in 2L of a 1.50 M CuSO₄ solution when it reacts with 27.0 grams of aluminium, we can follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between copper(II) sulfate (CuSO₄) and aluminium (Al) can be represented as:
\[ 3 \text{CuSO}_4 + 2 \text{Al} \rightarrow Al_2(SO_4)_3 + 3 \text{Cu} \]
This equation shows that 2 moles of aluminium will replace 3 moles of copper.

### Step 2: Calculate the number of moles of aluminium
To find the number of moles of aluminium, we use the formula:
\[ \text{Moles of Al} = \frac{\text{mass}}{\text{molar mass}} \]
Given that the molar mass of aluminium (Al) is 27.0 g/mol:
\[ \text{Moles of Al} = \frac{27.0 \text{ g}}{27.0 \text{ g/mol}} = 1.0 \text{ mol} \]

### Step 3: Determine the moles of copper that can be replaced
From the balanced equation, we know that 2 moles of Al replace 3 moles of Cu. Therefore, we can set up a ratio:
\[ \frac{3 \text{ mol Cu}}{2 \text{ mol Al}} \]
Now, using the moles of Al calculated:
\[ \text{Moles of Cu replaced} = 1.0 \text{ mol Al} \times \frac{3 \text{ mol Cu}}{2 \text{ mol Al}} = 1.5 \text{ mol Cu} \]

### Step 4: Calculate the mass of copper replaced
Now, we need to find the mass of copper that corresponds to the moles of copper replaced. The molar mass of copper (Cu) is 63.5 g/mol:
\[ \text{Mass of Cu} = \text{Moles of Cu} \times \text{Molar mass of Cu} \]
\[ \text{Mass of Cu} = 1.5 \text{ mol} \times 63.5 \text{ g/mol} = 95.25 \text{ g} \]

### Final Answer
Thus, the mass of copper that will be replaced is **95.25 grams**.

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